A new method to solve linear pulsation problems

An alternative method for calculating linear, non-adiabatic pulsations is proposed. It relies on the transformation of the liner two-point boundary eigenvalue problem to a numerically stable non-linear initial value problem where eigensolutions are determined by a shooting technique. Even for arbitrarily high overtones, the method proposed does not suffer from resolution problems and initial guesses for eigenvalue iteration are obtained without any reference to an approximation of the problem. By implicit solution the entire stellar model, including the very centre, is taken into account for the stability analysis. The superiority of the method is demonstrated for the example of a classical Cepheid. (author)